You got my interest going, so I googled it. And it lead me to the site of the creators of neoprene, which stated
Resists degradation from sun, ozone and weather
Performs well in contact with oils and many chemicals
Remains useful over a wide temperature range
Displays outstanding physical toughness
Resists burning inherently better than exclusively hydrocarbon rubbers
Outstanding resistance to damage caused by flexing and twisting
So it sounds like it won't melt or anything from friction. But I think you basically have to treat it like normal fabric.
Also, I pulled up this thread from cosplay.com that offers some good advice from some cosplay pros
http://forums.cosplay.com/showthread.php?t=11234&highlight=neopreneI hope that helped!